This paper presents growth orientation dependence of the piezoelectric polarization of InxGa1−xN and AlyGa1−yN layers lattice matched to GaN. This topic has become relevant with the advent of growing nitride based devices on semipolar planes [A. Chakraborty et al., Jpn. J. Appl. Phys., Part 2 44, L945 (2005)]. The calculations demonstrate that for strained InxGa1−xN and AlyGa1−yN layers lattice matched to GaN, the piezoelectric polarization becomes zero for nonpolar orientations and also at another point ≈45° tilted from the c plane. The zero crossover has only a very small dependence on the In or Al content of the ternary alloy layer. With the addition of spontaneous polarization, the angle at which the total polarization equals zero increases slightly for InxGa1−xN, but the exact value depends on the In content. For AlyGa1−yN mismatched layers the effect of spontaneous polarization becomes important by increasing the crossover point to ∼70° from c-axis oriented films. These calculations were performed using the most recent and convincing values for the piezoelectric and elasticity constants, and applying Vegard’s law to estimate the constants in the ternary InxGa1−xN and AlyGa1−yN layers.

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In the heteroepitaxial growth of films with large misfit with the underlying substrate ͑linear mismatch strains in excess of 1%-2%͒ the generation of misfit dislocations and threading dislocations ͑TDs͒ is ubiquitous for thicknesses well in excess of the equilibrium critical thickness. Experimental data suggest that the TD density in relaxed homogeneous buffer layers can be divided into three regimes: ͑i͒ an entanglement region near the film/substrate interface corresponding to TD densities of ϳ10 10 -10 12 cm Ϫ2 ; ͑ii͒ a falloff in TD density that is inversely proportional to the film thickness h, applicable to densities in the range ϳ10 7 -10 9 cm Ϫ2 ; and ͑iii͒ saturation or weak decay of the TD density with further increase in film thickness. Typical saturation densities are on the order of ϳ10 6 -10 7 cm Ϫ2 . In this article, we show that the TD reduction may be described in terms of effective lateral motion of TDs with increasing film thickness. An analytic model is developed that successfully predicts both the 1/h scaling behavior and the saturation of TD densities. Long-range fluctuations in the net Burgers vector content of the local TDs is a cause for saturation behavior. These models are supported by computer simulations.

This article presents a theoretical analysis of dislocation behavior and stress relaxation in semipolar III-nitride heteroepitaxy, e.g., for AlxGa1−xN and InyGa1−yN layers grown on {hh2−h−m}- or {h0h−m}-type semipolar planes of GaN substrates. We demonstrate that the shear stresses on the unique inclined basal (0001) plane do not vanish for such growth geometries. This leads to the onset of relaxation processes in semipolar III-nitride heterostructures via dislocation glide in the basal slip systems 〈1−1−20〉(0001) and to the formation of misfit dislocations (MDs) with Burgers vectors of (a/3)〈1−1−20〉-type at the semipolar heterointerface. Next we calculate the Matthews-Blakeslee critical thickness for MD formation in semipolar III-nitride layers together with the MD equilibrium spacings for complete misfit relaxation. The component of the MD Burgers vector normal to the film/substrate interface will cause a crystal lattice tilt in the epilayer with respect to the GaN substrate. The calculated magnitudes of the tilt angles are 0.62° and 0.67° for AlxGa1−xN and InyGa1−yN alloys with compositions of x = 0.20 and y = 0.07, respectively, grown in the (112−2) semipolar orientation. The modeling results are discussed in light of recent experimental observations [A. Tyagi et al., Appl Phys. Lett. 95, 251905 (2009); E. Young et al., Appl. Phys. Express 3, 011004 (2010); and F. Wu et al., J. Appl. Phys. 109, 033505 (2011)] of MDs and crystal lattice tilt in semipolar III-nitride heteroepitaxial layers.

Cathodoluminescence (CL) was used to study the onset of mechanical stress relaxation in low indium composition semipolar (112¯2) InxGa1−xN lattice-mismatched layers grown on bulk GaN substrates. Monochromatic CL of short interfacial misfit dislocation (MD) segments showed a single threading dislocation (TD) associated with each MD segment—demonstrating that the initial stage of MD formation in semipolar III-nitride heterostructures proceeded by the bending and glide of pre-existing TDs on the (0001) slip plane. The state of coherency as determined by panchromatic CL is also compared to that determined by x-ray diffraction analysis based on crystallographic epilayer tilt and Matthew-Blakeslee’s critical thickness calculations.

Epilayer lattice tilt has been observed by X-ray diffraction for heteroepitaxial AlGaN and InGaN films on (1122) semipolar GaN substrates. Complementary transmission electron microscopy demonstrates that epilayer tilt is a consequence of interfacial misfit dislocations with Burgers vectors a/3[1120] that glide on the (0001) basal plane [inclined ∼58° to (1122)]. The dislocation lines are parallel to [1100], consistent with the anisotropy of the tilt observed in X-ray scans parallel to orthogonal in-plane directions. The dislocations had an in-plane Burgers vector component that relieved misfit strain, and a perpendicular component responsible for lattice tilt. Dislocation densities predicted by tilt agree well with TEM measurements.